Connecting a face with another face along a specific curve
If it's a curve, then you'll need to convert the curve to a mesh by pressing "Alt+C".

Then choose "Convert Curve to Mesh".

Also make sure that each line of vertices has the same amount of vertices.

Press SpaceBar to bring up the search menu and type in "Bridge Edge Loops".

With both edges selected, click this function and the edges should form faces all the way along it.

I hope that answer provides your solution and happy modelling.

(EDIT)

Thanks for posting the screenshot of your problem.

This is rather more complicated and probably requires a bit more work than what I originally thought.

I made a pictoral tutorial, although I'm no expert on curves. I usually wing it though by playing around with the settings. Here's what I did to recreate your desired solution shown in the example below:


Here's the breakdown:



After I have all my edge loop cross sections, I apply the modifiers from top to bottom, in that order.

Then I join the edge loops (select them in object mode) with the main mesh (select the main mesh while holding Shift key and then press Ctrl+J).

In edit mode, I join all the edge loops together using "Bridge Edge Loops", then with some help from proportional editing, I spend 2-5 minutes playing with it a little (moving around some vertices or edge loops) and I also use "Smooth vertex" on some edge loops to smooth out the curvature which can be found in the ToolBar (T).

I hope this helps, and I'm sure this isn't the best or fastest workflow. Plus, curves are complicated and I'm no expert haha. There are probably better methods to do this but there are always 101 different ways to do things in blender. This is how I worked out the problem.

Good luck with it!